Geodesic
Refinements of the Littlewood-Richardson rule
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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We refine the classical Littlewood-Richardson rule in several different settings. We begin with a combinatorial rule for the product of a Demazure atom and a Schur function. Building on this, we also describe the product of a quasisymmetric Schur function and a Schur function as a positive sum of quasisymmetric Schur functions. Finally, we provide a combinatorial formula for the product of a Demazure character and a Schur function as a positive sum of Demazure characters. This last rule implies the classical Littlewood-Richardson rule for the multiplication of two Schur functions. 
@article{DMTCS_2009_special_256_a66,
     author = {Haglund, J. and Luoto, K. and Mason, S. and van Willigenburg, S.},
     title = {Refinements of the {Littlewood-Richardson} rule},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2744},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2744/}
}
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Haglund, J.; Luoto, K.; Mason, S.; van Willigenburg, S. Refinements of the Littlewood-Richardson rule. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2744. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2744/

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